02_basic_statistics.ipynb

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      "name": "ir",
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    "language_info": {
      "name": "R"
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  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
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      "source": [
        "<a href=\"https://colab.research.google.com/github/lisphilar/r_language/blob/main/02_basic_statistics.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# R language: basic statistics\n",
        "We will learn R language tools for basic statistics."
      ],
      "metadata": {
        "id": "6q_-mzMf8dGM"
      }
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
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        "id": "--jOfldn77fF",
        "outputId": "447337d0-5638-41b8-b0ef-f018e2b53883"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[1] \"R version 4.3.1 (2023-06-16)\"\n"
          ]
        }
      ],
      "source": [
        "print(R.version.string)"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "For cross table,"
      ],
      "metadata": {
        "id": "Hwb4G8ZAFKxA"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "install.packages(\"gmodels\")\n",
        "library(gmodels)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Hmys86MHFG7b",
        "outputId": "ee4f86db-4810-4488-cf64-5b23d6f8b750"
      },
      "execution_count": 2,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "Installing package into ‘/usr/local/lib/R/site-library’\n",
            "(as ‘lib’ is unspecified)\n",
            "\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Data structure"
      ],
      "metadata": {
        "id": "hUzk2sge84Ev"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "str(iris)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "BXuA377U8-qZ",
        "outputId": "4b776c7d-1869-4479-ebab-c249e14ec6eb"
      },
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "'data.frame':\t150 obs. of  5 variables:\n",
            " $ Sepal.Length: num  5.1 4.9 4.7 4.6 5 5.4 4.6 5 4.4 4.9 ...\n",
            " $ Sepal.Width : num  3.5 3 3.2 3.1 3.6 3.9 3.4 3.4 2.9 3.1 ...\n",
            " $ Petal.Length: num  1.4 1.4 1.3 1.5 1.4 1.7 1.4 1.5 1.4 1.5 ...\n",
            " $ Petal.Width : num  0.2 0.2 0.2 0.2 0.2 0.4 0.3 0.2 0.2 0.1 ...\n",
            " $ Species     : Factor w/ 3 levels \"setosa\",\"versicolor\",..: 1 1 1 1 1 1 1 1 1 1 ...\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "summary(iris)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 260
        },
        "id": "KWBE0vBs8qZq",
        "outputId": "8d94d1bc-c295-4815-b895-ee66e82ea122"
      },
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "  Sepal.Length    Sepal.Width     Petal.Length    Petal.Width   \n",
              " Min.   :4.300   Min.   :2.000   Min.   :1.000   Min.   :0.100  \n",
              " 1st Qu.:5.100   1st Qu.:2.800   1st Qu.:1.600   1st Qu.:0.300  \n",
              " Median :5.800   Median :3.000   Median :4.350   Median :1.300  \n",
              " Mean   :5.843   Mean   :3.057   Mean   :3.758   Mean   :1.199  \n",
              " 3rd Qu.:6.400   3rd Qu.:3.300   3rd Qu.:5.100   3rd Qu.:1.800  \n",
              " Max.   :7.900   Max.   :4.400   Max.   :6.900   Max.   :2.500  \n",
              "       Species  \n",
              " setosa    :50  \n",
              " versicolor:50  \n",
              " virginica :50  \n",
              "                \n",
              "                \n",
              "                "
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Categorical:"
      ],
      "metadata": {
        "id": "XtvTKVBnC1Ss"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "table(iris$Species)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 69
        },
        "id": "HKQkm-dsCr9h",
        "outputId": "0da3cee0-f048-4362-d280-4b021892c9a3"
      },
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "\n",
              "    setosa versicolor  virginica \n",
              "        50         50         50 "
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Percent:"
      ],
      "metadata": {
        "id": "1VaZjZn6EC5N"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "round(prop.table(table(iris$Species)) * 100, digits=1)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 69
        },
        "id": "K8Wjp0TIDCSH",
        "outputId": "1ce074b1-f3e3-4183-e5b5-b07c79209d36"
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      "execution_count": 6,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "\n",
              "    setosa versicolor  virginica \n",
              "      33.3       33.3       33.3 "
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Summary statistics"
      ],
      "metadata": {
        "id": "_CSkhJN2CIXb"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Five number summary:"
      ],
      "metadata": {
        "id": "cc6C-ylw_2Bv"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "summary(iris$Sepal.Length)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 52
        },
        "id": "28WZq2YD_4Ue",
        "outputId": "b5cf6ea0-53b3-4af6-c675-a050620f13d1"
      },
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. \n",
              "  4.300   5.100   5.800   5.843   6.400   7.900 "
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Mean:"
      ],
      "metadata": {
        "id": "NTzsiDDT_l2a"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "mean(iris$Sepal.Length)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "id": "Q-6g7K0w_lPC",
        "outputId": "9bf36216-5048-4775-fb22-d6218c458294"
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      "execution_count": 8,
      "outputs": [
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              "5.84333333333333"
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            "text/markdown": "5.84333333333333",
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              "[1] 5.843333"
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      "source": [
        "Median:"
      ],
      "metadata": {
        "id": "SAZbeXE3_ujD"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "median(iris$Sepal.Length)"
      ],
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          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "id": "aD0NGrNA_uDa",
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      "source": [
        "Range from min to max:"
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      "cell_type": "code",
      "source": [
        "range(iris$Sepal.Length)"
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          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "id": "3l79YClo_cGW",
        "outputId": "5136a548-09d1-4a17-a5db-9629659b62ea"
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      "execution_count": 10,
      "outputs": [
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              "<ol class=list-inline><li>4.3</li><li>7.9</li></ol>\n"
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              "[1] 4.3 7.9"
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        "IQR (interquantile range):"
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      "cell_type": "code",
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        "Quntile:"
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      "metadata": {
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    {
      "cell_type": "code",
      "source": [
        "quantile(iris$Sepal.Length)"
      ],
      "metadata": {
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          "base_uri": "https://localhost:8080/",
          "height": 34
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        "id": "Sm03i3OlA-Nu",
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              "</style><dl class=dl-inline><dt>0%</dt><dd>4.3</dd><dt>25%</dt><dd>5.1</dd><dt>50%</dt><dd>5.8</dd><dt>75%</dt><dd>6.4</dd><dt>100%</dt><dd>7.9</dd></dl>\n"
            ],
            "text/markdown": "0%\n:   4.325%\n:   5.150%\n:   5.875%\n:   6.4100%\n:   7.9\n\n",
            "text/latex": "\\begin{description*}\n\\item[0\\textbackslash{}\\%] 4.3\n\\item[25\\textbackslash{}\\%] 5.1\n\\item[50\\textbackslash{}\\%] 5.8\n\\item[75\\textbackslash{}\\%] 6.4\n\\item[100\\textbackslash{}\\%] 7.9\n\\end{description*}\n",
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      "cell_type": "code",
      "source": [
        "quantile(iris$Sepal.Length, prob=c(0.01, 0.99))"
      ],
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        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
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              ".dl-inline>dt, .dl-inline>dd {float: none; width: auto; display: inline-block}\n",
              ".dl-inline>dt::after {content: \":\\0020\"; padding-right: .5ex}\n",
              ".dl-inline>dt:not(:first-of-type) {padding-left: .5ex}\n",
              "</style><dl class=dl-inline><dt>1%</dt><dd>4.4</dd><dt>99%</dt><dd>7.7</dd></dl>\n"
            ],
            "text/markdown": "1%\n:   4.499%\n:   7.7\n\n",
            "text/latex": "\\begin{description*}\n\\item[1\\textbackslash{}\\%] 4.4\n\\item[99\\textbackslash{}\\%] 7.7\n\\end{description*}\n",
            "text/plain": [
              " 1% 99% \n",
              "4.4 7.7 "
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          "metadata": {}
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    {
      "cell_type": "markdown",
      "source": [
        "Var:"
      ],
      "metadata": {
        "id": "LNjmsWL5CSAx"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "var(iris$Sepal.Length)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "id": "dDI3THkiCc7W",
        "outputId": "314ca431-03bd-4be6-a3d2-207d21f4f498"
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      "execution_count": 14,
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              "[1] 0.6856935"
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    },
    {
      "cell_type": "markdown",
      "source": [
        "SD:"
      ],
      "metadata": {
        "id": "wpqVGFAsCaoh"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "sd(iris$Sepal.Length)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "id": "YOZK588KCfqf",
        "outputId": "8c208f97-6633-4059-f477-c9e9abe12cf2"
      },
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "0.828066127977863"
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            "text/markdown": "0.828066127977863",
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              "[1] 0.8280661"
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    {
      "cell_type": "markdown",
      "source": [
        "Mode:"
      ],
      "metadata": {
        "id": "eu1AmIjIENHz"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Plot"
      ],
      "metadata": {
        "id": "kA2K0SRnCEMz"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Box plot"
      ],
      "metadata": {
        "id": "UroE7D5ZBG_v"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "boxplot(iris$Sepal.Length, main=\"Boxplot of Sepal Length\", ylab=\"length [cm]\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 437
        },
        "id": "WNso-3EQBQb2",
        "outputId": "ccd3d65f-c713-4894-adce-abb909a2f745"
      },
      "execution_count": 16,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "Plot with title “Boxplot of Sepal Length”"
            ],
            "image/png": 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korQrK0+d3fzxV11bcXnTmsX+XAcX+1PnEYIaUVIVna/EQq9o19nUJIaUVIFjuk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\nAf8fT3l+JbhtlKUAAAAASUVORK5CYII="
          },
          "metadata": {
            "image/png": {
              "width": 420,
              "height": 420
            }
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Histogram"
      ],
      "metadata": {
        "id": "ONh1EunZBvQ4"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "hist(iris$Sepal.Length, main=\"Histogran of Sepal Lenghth\", xlab=\"length [cm]\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 437
        },
        "id": "ozl9ox7SBxGc",
        "outputId": "6977599d-9578-4ce1-c01d-71aeae051ba2"
      },
      "execution_count": 17,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "Plot with title “Histogran of Sepal Lenghth”"
            ],
            "image/png": 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kogpDyWckgV5QWXx7ZOjxQtD9mRkBII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\nCTUR0r1PfBRyr6VPjCKkFkRIiiQV0jrzlNdkSB/u4o5TCakFEZI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          },
          "metadata": {
            "image/png": {
              "width": 420,
              "height": 420
            }
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Scatterplot"
      ],
      "metadata": {
        "id": "g0JPweGeEa-j"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "plot(\n",
        "    x=iris$Sepal.Length, y=iris$Sepal.Width,\n",
        "    main=\"Sepal: Width vs. Length\", xlab=\"Length [cm]\", ylab=\"Width [cm]\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 437
        },
        "id": "bRTkWKqCB4fV",
        "outputId": "29cd33ea-92fd-413d-c328-8ea4b42632c2"
      },
      "execution_count": 18,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "Plot with title “Sepal: Width vs. Length”"
            ],
            "image/png": 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ucRoDESTwM/qP2qXtTGxk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          },
          "metadata": {
            "image/png": {
              "width": 420,
              "height": 420
            }
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Cross table"
      ],
      "metadata": {
        "id": "K8Bghl1pE6WJ"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "str(UCBAdmissions)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "oiremrxIEyYV",
        "outputId": "b76608c9-274c-494c-9da2-c4c39eff32e6"
      },
      "execution_count": 19,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            " 'table' num [1:2, 1:2, 1:6] 512 313 89 19 353 207 17 8 120 205 ...\n",
            " - attr(*, \"dimnames\")=List of 3\n",
            "  ..$ Admit : chr [1:2] \"Admitted\" \"Rejected\"\n",
            "  ..$ Gender: chr [1:2] \"Male\" \"Female\"\n",
            "  ..$ Dept  : chr [1:6] \"A\" \"B\" \"C\" \"D\" ...\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "raw <- data.frame(UCBAdmissions)\n",
        "str(raw)\n",
        "print(raw)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "E68Sr5TMGJZG",
        "outputId": "f27a2b95-e94a-484d-dd0c-3447211f30a2"
      },
      "execution_count": 20,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "'data.frame':\t24 obs. of  4 variables:\n",
            " $ Admit : Factor w/ 2 levels \"Admitted\",\"Rejected\": 1 2 1 2 1 2 1 2 1 2 ...\n",
            " $ Gender: Factor w/ 2 levels \"Male\",\"Female\": 1 1 2 2 1 1 2 2 1 1 ...\n",
            " $ Dept  : Factor w/ 6 levels \"A\",\"B\",\"C\",\"D\",..: 1 1 1 1 2 2 2 2 3 3 ...\n",
            " $ Freq  : num  512 313 89 19 353 207 17 8 120 205 ...\n",
            "      Admit Gender Dept Freq\n",
            "1  Admitted   Male    A  512\n",
            "2  Rejected   Male    A  313\n",
            "3  Admitted Female    A   89\n",
            "4  Rejected Female    A   19\n",
            "5  Admitted   Male    B  353\n",
            "6  Rejected   Male    B  207\n",
            "7  Admitted Female    B   17\n",
            "8  Rejected Female    B    8\n",
            "9  Admitted   Male    C  120\n",
            "10 Rejected   Male    C  205\n",
            "11 Admitted Female    C  202\n",
            "12 Rejected Female    C  391\n",
            "13 Admitted   Male    D  138\n",
            "14 Rejected   Male    D  279\n",
            "15 Admitted Female    D  131\n",
            "16 Rejected Female    D  244\n",
            "17 Admitted   Male    E   53\n",
            "18 Rejected   Male    E  138\n",
            "19 Admitted Female    E   94\n",
            "20 Rejected Female    E  299\n",
            "21 Admitted   Male    F   22\n",
            "22 Rejected   Male    F  351\n",
            "23 Admitted Female    F   24\n",
            "24 Rejected Female    F  317\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "df <- data.frame(lapply(raw, function(i){rep(i, raw[, 4])}))[-4]\n",
        "str(df)\n",
        "print(df[1:5,])"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "J3m_AJg0FEnW",
        "outputId": "9fc06ed3-20cb-43c5-85d6-fc1334c6685f"
      },
      "execution_count": 21,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "'data.frame':\t4526 obs. of  3 variables:\n",
            " $ Admit : Factor w/ 2 levels \"Admitted\",\"Rejected\": 1 1 1 1 1 1 1 1 1 1 ...\n",
            " $ Gender: Factor w/ 2 levels \"Male\",\"Female\": 1 1 1 1 1 1 1 1 1 1 ...\n",
            " $ Dept  : Factor w/ 6 levels \"A\",\"B\",\"C\",\"D\",..: 1 1 1 1 1 1 1 1 1 1 ...\n",
            "     Admit Gender Dept\n",
            "1 Admitted   Male    A\n",
            "2 Admitted   Male    A\n",
            "3 Admitted   Male    A\n",
            "4 Admitted   Male    A\n",
            "5 Admitted   Male    A\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "CrossTable(x=df$Dept, y=df$Admit)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "SevwhR50HJYn",
        "outputId": "d041d2d8-3f73-4214-9d09-ee68a0959275"
      },
      "execution_count": 22,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            " \n",
            "   Cell Contents\n",
            "|-------------------------|\n",
            "|                       N |\n",
            "| Chi-square contribution |\n",
            "|           N / Row Total |\n",
            "|           N / Col Total |\n",
            "|         N / Table Total |\n",
            "|-------------------------|\n",
            "\n",
            " \n",
            "Total Observations in Table:  4526 \n",
            "\n",
            " \n",
            "             | df$Admit \n",
            "     df$Dept |  Admitted |  Rejected | Row Total | \n",
            "-------------|-----------|-----------|-----------|\n",
            "           A |       601 |       332 |       933 | \n",
            "             |   158.180 |   100.183 |           | \n",
            "             |     0.644 |     0.356 |     0.206 | \n",
            "             |     0.342 |     0.120 |           | \n",
            "             |     0.133 |     0.073 |           | \n",
            "-------------|-----------|-----------|-----------|\n",
            "           B |       370 |       215 |       585 | \n",
            "             |    90.350 |    57.223 |           | \n",
            "             |     0.632 |     0.368 |     0.129 | \n",
            "             |     0.211 |     0.078 |           | \n",
            "             |     0.082 |     0.048 |           | \n",
            "-------------|-----------|-----------|-----------|\n",
            "           C |       322 |       596 |       918 | \n",
            "             |     3.241 |     2.052 |           | \n",
            "             |     0.351 |     0.649 |     0.203 | \n",
            "             |     0.183 |     0.215 |           | \n",
            "             |     0.071 |     0.132 |           | \n",
            "-------------|-----------|-----------|-----------|\n",
            "           D |       269 |       523 |       792 | \n",
            "             |     4.728 |     2.995 |           | \n",
            "             |     0.340 |     0.660 |     0.175 | \n",
            "             |     0.153 |     0.189 |           | \n",
            "             |     0.059 |     0.116 |           | \n",
            "-------------|-----------|-----------|-----------|\n",
            "           E |       147 |       437 |       584 | \n",
            "             |    27.876 |    17.655 |           | \n",
            "             |     0.252 |     0.748 |     0.129 | \n",
            "             |     0.084 |     0.158 |           | \n",
            "             |     0.032 |     0.097 |           | \n",
            "-------------|-----------|-----------|-----------|\n",
            "           F |        46 |       668 |       714 | \n",
            "             |   192.503 |   121.921 |           | \n",
            "             |     0.064 |     0.936 |     0.158 | \n",
            "             |     0.026 |     0.241 |           | \n",
            "             |     0.010 |     0.148 |           | \n",
            "-------------|-----------|-----------|-----------|\n",
            "Column Total |      1755 |      2771 |      4526 | \n",
            "             |     0.388 |     0.612 |           | \n",
            "-------------|-----------|-----------|-----------|\n",
            "\n",
            " \n"
          ]
        }
      ]
    }
  ]
}